Basic question: meaning of partition of R into maximal connected intervals

seeker101
Messages
28
Reaction score
0
Basic question: meaning of "partition of R into maximal connected intervals"

What does the phrase "partition of R into maximal connected intervals" mean?

The full sentence: "Let I_1, I_2, ... ,I_m be the partition of R into maximal connected intervals with disjoint interiors."
 
Mathematics news on Phys.org


Without knowing the context, it appears the author means that it is not possible to add another interval to the finite sequence that is connected and has disjoint interior. Ie., I1 = (-oo, 0], I2 = [0, oo).
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »
Thread 'Imaginary Pythagorus'

Thread 'Imaginary Pythagorus'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
View full post »

Similar threads

I Simple partitioning of sequence in Proposition 1.15 in Folland's text
Replies
3
Views
2K
I Collection of finite unions of half-open intervals form an algebra
Replies
3
Views
3K
I Two basic results from measure theory -- on volumes of rectangles
Replies
2
Views
2K
I Meaning of "passage to the quotient"?
Replies
3
Views
448
I Attempting to find an intuitive proof of the substitution formula
Replies
7
Views
2K
I Measurement of heat as an interval measurement or a ratio measurement
Replies
9
Views
3K
Proof involving partitions and equivalence class
Replies
2
Views
1K
I Can chatgpt accurately calculate expected lengths in Pascal's triangle?
2
Replies
66
Views
6K
I Partition Function: 2 Approaches & Questions Answered
Replies
9
Views
2K
I Feynman's probability lecture -- a few questions
Replies
17
Views
3K

Hot Threads

Recent Insights

Back
Top